Question

A recreational equipment supplier inds that among orders that include tents, 40% also include sleeping mats. Only 5% of orders that do not include tents do include sleeping mats. Also, 20% of orders include tents. Determine the following probabilities:

a. The order includes sleeping mats.
b. The order includes a tent given it includes sleeping mats.

Answer 1

a. 12%

b. 2/3

Explanation:

Given data regarding orders that do and don't include tents and/or mats, you want to find the probabilities of (a) the order includes mats; (b) the order includes a tent given that it includes mats.

Two-way table

The given data is summarized in the attached two-way table. The value in blue is given in the problem statement. The values in purple are computed from values given in the problem:

40% of the 20% of orders include a tent and mat = 8% of orders

5% of the 80% of orders with no tent = 4% of orders include a mat

The numbers in black make the totals come out right.

a. Includes mat

The table shows that 8% +4% = 12% of all orders include sleeping mats.

P(m) = 12%

b. Includes tent, given includes mats

8% of the 12% of orders that include mats also include a tent. The probability of an order including a tent given that it includes a mat is ...

P(t|m) = 8%/12% = 2/3